Question

A box contains 10 balls. Three of them are white, five are red, and two are
black. Calculate the following probabilities:
a) The first ball extracted is red.
b) The first ball extracted is red or white.
c) The second ball extracted is red given that the first is white (with replacement).
d) The second ball extracted is red given that the first is white (without replacement).
e) The second ball extracted is red given that the first is also red (without
replacement).
f) How many samples of three balls can be extracted from this population? Assume that you are extracting one sample of size three

Answer 1

A box contains 10 balls. Three of them are white, five are red, and two are
black. Calculate the following probabilities:
a) The first ball extracted is red.
b) The first ball extracted is red or white.
c) The second ball extracted is red given that the first is white (with replacement).
d) The second ball extracted is red given that the first is white (without replacement).
e) The second ball extracted is red given that the first is also red (without
replacement).
f) How many samples of three balls can be extracted from this population? Assume that you are extracting one sample of size three

Answer 2

a) prob(red) = 5/10 = 1/2
b) prob(red or white) = 7/10
c) prob( as stated) = 5/10 or 1/2 , there are still 10 balls, since you replaced it whatever happened in first draw has no effect on the second draw
d) prob( as stated) = 5/9 , now it matters, there are only 9 balls left
e) 4 reds left, 9 in total, so prob = 4/9


f)
We can list them, there are only a few

WWW
RRR
BBB
WWR
WWB
RRW
RRB
BBW
BBR
WRB